11. Multiply 3 £. 4 s. 6 d. by 7. 13. What will be the cost of 5 pairs of shoes at 10 s. 6 d. a pair? 15. In 5 barrels of wheat, each containing 2 bu. 3 pks. 6 qts., how many bushels? 17. How many yards of cloth 18. If 9 coats contain 39 yds. 3 will be required for 9 coats, allow-qrs. 3 na., what does 1 coat coning 4 yds. 1 qr. 3 na. to each 19. In 7 bottles of wine, each containing 2 qts. 1 pt. 3 gills, how many gallons? 21. What will be the weight of 8 silver cups, each weighing 5 oz. 12 pwt. 17 grs. ? 23. How much sugar in 12 hogsheads, each containing 9 cwt. 3 qrs. 21 lb. ? 25. In 15 loads of hay, each weighing 1 T. 3 cwt. 2 qrs., how many tons? tain? 20. If 5 gal. 1 gill of wine be divided equally into 7 bottles, how much will each contain ? 22. If 8 silver cups weigh 3 lb. 9 oz. 1 pwt. 16 grs., what is the weight of each? 24. If 119 cwt. 1 qr. of sugar be divided into 12 hogsheads, how much will each hogshead contain? 26. If 15 teams be loaded with 17 T. 12 cwt. 2 qrs. of hay, how much is that to each team? When the multiplier or divisor exceeds 12, the operations of multiplying and dividing are not so easy, unless they be composite numbers; in that case, we may make use of the component parts, or factors, as was done in simple numbers. 31. How much brandy in 841 pipes, each containing 112 gal. 2 qts. 1 pt. 3 g.? 33. What will 139 yards of cloth cost, at 3 £. 6 s. 5 d. per yard? 139 is not a composite number. We may, however, decompose this number thus, 139 100+ 30+9. We may now multiply the price of 1 yard by 10, which will give the price of 10 yards, and this product again by 10, which will give the price of 100 yards. We may then multiply the price of 10 yards by 3, which will give the price of 30 yards, and the price of 1 yard by 9, which will give the price of 9 yards, and these three products, added together, will evidently give the price of 139 yards; thus: £. s. d. 3 33 332 6 5 price of 1 yard. 10 4 2 price of 10 yds. 1 99 12 29 17 10 8 price of 100 yds. 461 11 11 price of 139 yds. Note. In multiplying the price of 10 yards (33 £. 4 s. 2 d.) by 3, to get the price of 30 yards, and in multiplying the price of 1 yard (3 £. 6 s. 5 d.) by 9, to get the price of 9 yards, the multipliers, 3 and 9, need not be written down, but may be carried in the mind. The divisor, 139, is contained in 461 £. 3 times, (3 £.,) and a remainder of 44 £., which must now be reduced to shillings, multiplying it by 20, and bringing in the given shillings, (11 s.,) making 891 s., in which the divisor is contained 6 times, (6 s.,) and a remainder of 57 s., which must be reduced to pence, multiplying it by 12, and bringing in the giver pence, (11 d.,) together making 695 d., in which the divisor is contained 5 times, (5 d.,) and no remainder. The several quotients, 3 £., 6 s., 5 d., evidently make the an swer. The processes in the foregoing examples may now be presented in the form of a. RULE for the Multiplication of RULE for the Division of ComCompound Numbers. pound Numbers. I. When the multiplier does I. When the divisor does not not exceed 12, multiply succes-exceed 12, m the manner of short sively the numbers of each deno-division, find how many times it mination, beginning with the is contained in the highest denoleast, as in multiplication of sim- mination, under which write the ple numbers, and carry as in ad-quotient, and, if there be a redition of compound numbers, set-mainder, reduce it to the next less ting down the whole product of the highest denomination. II. If the multiplier exceed 12, and be a composite number, we may multiply first by one of the component parts, that product by another, and so on, if the component parts be more than two; the last product will be the product required. denomination, adding thereto the number given, if any, of that denomination, and divide as before; so continue to do through all the denominations, and the several quotients will be the answer. II. If the divisor exceed 12, and be a composite, we may divide first by one of the component parts, that quotient by another, and so on, if the component parts be more than two; the last quotient will be the quotient requir ed. III. When the multiplier ex- III. When the divisor exceeds ceeds 12, and is not a composite, 12, and is not a composite nummultiply first by 10, and this pro-ber, divide after the manner of duct by 10, which will give the long division, setting down the product for 100; and if the hun-work of dividing and reducing. dreds in the multiplier be more than one, multiply the product of 100 by the number of hundreds; for the tens, multiply the product of 10 by the number of tens; for the units, multiply the multiplicand; and these several prodvets will be the product required. EXAMPLES FOR PRACTICE. 1. What will 359 yards of cloth | 2. Bought 359 yards of cloth cost at 4 s. 7 d. per yard? for 83 £.0 s. 4 d.; what was that a yard? 3. In 241 barrels of flour, each containing 1 cwt. 3 qr. 9 lb., how many cwt.? 5. How many bushels of wheat in 135 bags, each containing 2 bu. 3 pks. ? 3 X 9 X 5 135. 7. What will 35 cwt. of tobacco cost at 3 s. 10 d. per lb.? 9. If 14 men build 12 rods 6 feet of wall in one day, how many rods will they build in 7 days?" 4. If 441 cwt. 13 lb. of flour be contained in 241 barrels, how much in a barrel? 6. If 371 bu. 1 pk. of wheat be divided equally into 135 bags how much will each bag contain? 8. At 759 £. 10 s. for 35 cwt. of tobacco, what is that per lb. ? 10. If 14 men build 92 rods 12 feet of stone wall in 7 days, how much is that per day? ¶ 42. 1. At 10 s. per yard, what will 17849 yards of cloth cost? Note. Operations in multiplication of pounds, shillings, pence, or of any compound numbers, may be facilitated by taking aliquot parts of a higher denomination, as already explained in "Practice" of Federal Money, ¶ 29, ex. 10. Thus, in this last example, the price 10 s. of a pound; therefore, of the number of yards will be the cost in pounds. 17849: 8924 £. 10 s. Ans. at 4 s. 2. What cost 34648 yards of cloth, at 10 s. or £. per yard? at 5 s.£. per yard? £. per yard? yard? at 3 s. 4 d. = 3. What cost 7430 pounds of sugar at 6 d. = at 4 d. d. = Fs. per lb.? s. per lb.? £. per yard? TO £. 16 s. £. per at 2 s."= Ans. to last, 3464 = s. per lb. ? at 3 d. at 1 d. = 4s. per lb. ? at 2 s. per lb.? cwt. cost? cwt. what will 8 $1875 = $1′339+, Ans. to the last. 5. What cost 340 yards of cloth, at 12 s. 6 d. per yard? 12 s. 6 d. = 10 s. (= § £.) and 2 s. 6 d. (= 1. What distinction do you make hetween simple and compound aumbers? ( 26.) 2. What is the rule for addition of compound numbers? 3. for subtraction of, &c. ? 4. There are three conditions in the rule given for multiplication of compound numbers; what are they, and the methods of procedure under each? 5. The same questions in respect to the division of compound numbers. 6. When the multiplier or divisor is encumbered with a fraction, how do you proceed? 7. How is the distance of time from one date to another found? 8. How many degrees does the earth revolve from west to east in 1 hour? 9. In what time does it revolve 1°? Where is the time or hour of the day earlier at the place most easterly or most westerly? 10. The difference in longitude between two places being known, how is the difference in time calculated? 11. How may operations, in the multiplication of compound numbers, be faci litated? 12. What are some of the aliquot parts of 1 £.? of 1 cwt.? 13. What is this manner of operatin of 1 s. ? EXERCISES. 1. A gentleman is possessed of 11⁄2 dozen of silver spoons, each weighing 3 oz. 5 pwt.; 2 doz. of tea spoons, each weighing 15 pwt. 14 gr.; 3 silver cans, each 9 oz. 7 pwt.; 2 silver tankards, each 21 oz. 15 pwt.; and 6 silver porringers, each 11 oz. 18 pwt.; what is the weight of the whole? Ans. 18 lb. 4 oz. 3 pw Note. Let the pupi. be required to reverse aua prove me following examples. 2. An English guinea should weigh 5 pw. 6 gr.; a piece or goid weighs 3 pwt. 17 gr.; how much is that short of the weight of a guinea? 3. What is the weight of 6 chests of tea, each weighing 3 cwt. 2 qrs. 9 lb. ? 4. In 35 pieces of cloth, each measuring 27 yards, how many yards? 5. How much brandy in 9 casks, each containing 35 gal. 3 qts. 1 pt. ? 6. If 31 cwt. 2 qrs. 20 lb. of sugar be distributed equally into 4 casks, how much will each contain? 7. At 41 d. per lb., what costs 1 cwt. of rice? 3 cwt. 2 cwt. ? Note. The pupil will recollect that 8, 7, and 2, are factors of 112 and may be used in place of that number. 8. If 8 cwt. of cocoa cost 18 £. 13 s. 4 d., what is that per cwt ↑ what is it per lb.? 9. What will 94 cwt. of copper cost at 5 s. 9 d. per lb. ? 10. If 6 cwt. of chocolate cost 72 £. 16 s., what is that per lb. ? 11. What cost 456 bushels of potatoes, at 2 s. 6 d. per bushel? Note. 2 s. 6 d. is 1 of 1 £. (See T 42.) 180 12. What cost 86 yards of broadcloth, at 15 s. per yard? Note. Consult T 42, ex. 5. 13. What cost 7846 pounds of tea, at 7 s. 6 d. per lb. ? 14 s. per lb. ? at 13 s. 4 d. ? at 14. At $94 25 per cwt. what will be the cost of 2 qrs. of tea? of 21 lbs. ? of 3 qrs.? of 16 lbs. ? of 14 lbs. ? of 24 lbs. ? Note. Consult T 42, ex. 4 and 5. 15. What will be the cost of 2 pks, and 4 qts. of wheat, at $ 1'50 per bushel? |